Why can slowly grown quasicrystals have more perfect order than rapidly cooled ones?

Slowly grown quasicrystals achieve higher perfection because they allow the material to reach thermodynamic equilibrium, whereas rapid cooling often traps the structure in a disordered state.1

In quasicrystals, there exists a specific type of elastic deformation known as a phason, which corresponds to rearrangements of relative atomic positions. At low temperatures, atomic motion is restricted, causing these phason strains to become "frozen" into the structure, which limits its overall perfection.2

Conversely, when quasicrystals are grown slowly and carefully at temperatures close to the melting point, phasons are able to fluctuate and atoms can jump between positions. This process allows the material to minimize its free energy and develop more perfect rotational symmetry and quasiperiodicity. In contrast, rapidly cooled alloys—such as the original aluminum-manganese samples—are often caught out of equilibrium, resulting in less perfect ordering.12